General Chemistry 1050: Thermochemistry, Atomic Structure, and Quantum Theory Study Notes

Thermochemistry

Enthalpy Changes and Thermochemical Equations

Thermochemistry deals with the heat changes that accompany chemical reactions. The enthalpy change ($\Delta H$) for a reaction is a key concept, representing the heat absorbed or released at constant pressure.

• Thermochemical Equation: A balanced chemical equation that includes the enthalpy change.

• Standard Enthalpy of Reaction ($\Delta_r H^\circ$): The enthalpy change when reactants in their standard states form products in their standard states.

• Hess's Law: The total enthalpy change for a reaction is the same, no matter how many steps the reaction is carried out in.

Example: Calculating $\Delta_r H^\circ$ using a series of thermochemical equations or using standard enthalpies of formation ($\Delta_f H^\circ$).

• Standard Enthalpy of Formation ($\Delta_f H^\circ$): The enthalpy change when one mole of a compound forms from its elements in their standard states.

Formula:

$\Delta_r H^\circ = \sum \Delta_f H^\circ (\text{products}) - \sum \Delta_f H^\circ (\text{reactants})$

Property Highlighted: The state function property of enthalpy, meaning the enthalpy change depends only on the initial and final states, not the path taken.

Atomic Structure and Electron Configuration

Electron Configurations and Orbital Diagrams

Electron configuration describes the arrangement of electrons in an atom's orbitals. The Aufbau principle, Pauli exclusion principle, and Hund's rule govern the filling of atomic orbitals.

• Aufbau Principle: Electrons fill orbitals starting with the lowest energy first.

• Pauli Exclusion Principle: No two electrons in an atom can have the same set of four quantum numbers.

• Hund's Rule: Electrons occupy degenerate orbitals singly before pairing up.

Example: Writing electron configurations for Si, Y3+, and Cu.

Quantum Numbers

Each electron in an atom is described by four quantum numbers:

• Principal quantum number ($n$): Indicates the energy level (shell).

• Azimuthal quantum number ($l$): Indicates the subshell (s, p, d, f).

• Magnetic quantum number ($m_l$): Indicates the specific orbital within a subshell.

• Spin quantum number ($m_s$): Indicates the spin direction (+1/2 or -1/2).

Paramagnetism and Diamagnetism

• Paramagnetic: Atoms or ions with unpaired electrons; attracted to a magnetic field.

• Diamagnetic: Atoms or ions with all electrons paired; weakly repelled by a magnetic field.

Radial Probability Distributions and Nodes

Radial probability distributions show the probability of finding an electron at a certain distance from the nucleus. Nodes are regions where the probability is zero.

• Radial Nodes: Spherical regions where the probability of finding an electron is zero; number of radial nodes = $n - l - 1$.

• Angular Nodes: Planar regions (for p, d, f orbitals) where the probability is zero; number of angular nodes = $l$.

Example: Comparing 2s and 2p orbitals in terms of energy and node structure.

Atomic Spectra and the Bohr Model

Energy Levels and Electron Transitions

When electrons transition between energy levels in an atom, they absorb or emit photons of specific energies, producing atomic spectra.

• Bohr Model: Electrons occupy quantized energy levels; transitions between levels result in absorption or emission of photons.

• Energy of a Photon: $E = h\nu = \frac{hc}{\lambda}$

• Rydberg Formula for Hydrogen-like Atoms:

$E_{n} = -2.179 \times 10^{-18} \frac{Z^2}{n^2}$

$\Delta E = E_{n_f} - E_{n_i}$

Frequency of Emitted Photon:

$\nu = \frac{\Delta E}{h}$

Visible Light Range: 400–750 nm. Transitions that emit photons in this range are visible to the human eye.

Calorimetry and Heat Measurement

Bomb Calorimetry

Calorimetry is the measurement of heat flow. A bomb calorimeter is used to measure the change in internal energy ($\Delta U$) for combustion reactions at constant volume.

• Heat Capacity ($C$): The amount of heat required to raise the temperature of the calorimeter by 1 K.

• Calculation: $q = C \Delta T$

• Relationship: For bomb calorimetry, $\Delta U = q_v$ (since $w = 0$ at constant volume).

Example: Calculating the final temperature in a bomb calorimeter after combustion of a known mass of benzoic acid.

Relationship Between $\Delta U$ and $\Delta H$

At constant pressure, the enthalpy change ($\Delta H$) is related to the internal energy change ($\Delta U$) by:

$\Delta H = \Delta U + \Delta n_g RT$

where $\Delta n_g$ is the change in moles of gas.

Significant Figures and Units

Reporting Results

All numerical answers in chemistry must be reported with the correct number of significant figures and appropriate units. Marks may be deducted for incorrect use of significant figures.

• Significant Figures: Reflect the precision of measured or calculated values.

• Units: Always include units in final answers (e.g., kJ, mol, K).

Reference Tables

Periodic Table

The periodic table organizes elements by increasing atomic number and groups elements with similar chemical properties.

Physical Constants and Useful Formulas

Quantity and Symbol	Value
Rydberg constant, R	1.0973 × 107 m−1
Planck's constant, h	6.626 × 10−34 J·s
Avogadro's constant, NA	6.022 × 1023 mol−1
Ideal Gas Constant, R	8.314 J·mol−1·K−1
Speed of light, c	2.998 × 108 m·s−1

Useful Formulas:

• $PV = nRT$ (Ideal Gas Law)

• $E = h\nu$ (Energy of a photon)

• $\Delta E = -2.179 \times 10^{-18} Z^2 \left( \frac{1}{n_f^2} - \frac{1}{n_i^2} \right)$ (Energy change for hydrogen-like atoms)

• $q = C \Delta T$ (Calorimetry)

• $\Delta H = \sum \Delta_f H^\circ (\text{products}) - \sum \Delta_f H^\circ (\text{reactants})$ (Enthalpy of reaction)